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Convergence conditions for iterative methods seeking multi-component solitary waves with prescribed quadratic conserved quantities
T. I. Lakoba
We obtain local (i.e., linearized) convergence conditions for iterative methods that seek solitary waves with prescribed values of quadratic conserved quantities of multi-component…
Accelerated Imaginary-time Evolution Methods for the Computation of Solitary Waves
Jianke Yang, Taras I. Lakoba
Two accelerated imaginary-time evolution methods are proposed for the computation of solitary waves in arbitrary spatial dimensions. For the first method (with traditional power no…
A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity
T. I. Lakoba, J. Yang
The Petviashvili's iteration method has been known as a rapidly converging numerical algorithm for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave…
A mode elimination technique to improve convergence of iteration methods for finding solitary waves
T. I. Lakoba, J. Yang
We extend the key idea behind the generalized Petviashvili method of Ref. \cite{gP} by proposing a novel technique based on a similar idea. This technique systematically eliminates…
Universally-convergent Squared-operator Iteration Methods for Solitary Waves in General Nonlinear Wave Equations
Jianke Yang, Taras Lakoba
Three new iteration methods, namely the squared-operator method, the modified squared-operator method, and the power-conserving squared-operator method, for solitary waves in gener…